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In this paper we analyze the impact that energy-saving strategies, like the application of DVFS via Linux governors and the MPI communication mode, have on the performance and energy consumption of message-passing dense linear algebra operations. In the study, we employ codes from ScaLAPACK for three matrix kernels, the matrix-matrix and matrix-vector products and the Cholesky factorization, which exhibit different levels of concurrency and CPU/memory activity. Following a recent trend, we also include an accelerated version of the matrix-matrix product that off-loads all computation to a graphics processor and study the energy gains of this hybrid solver when the general-purpose cores of the system are promoted to a low consuming mode. Experimental results on a cluster equipped with state-of-the-art computation and communication hardware illustrate the results of this study.